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L'étude porte sur l'impact de vagues sur une paroi rigide en deux dimensions. Les travaux de modélisation numérique ont été réalisés à partir du code JOSEPHINE, utilisant la méthode Smoothed Particle Hydrodynamics (SPH), développé au sein du laboratoire LOMC. La méthode choisie repose sur une approximation faiblement compressible des équations d'Euler. Dans un premier temps, l'étude d'un cas académique de l'impact d'un jet triangulaire a permis de valider et améliorer le schéma numérique permettant la modélisation d'impacts violents. Les pressions d'impacts ont été étudiées et comparées à d'autres résultats analytiques et numériques. Dans un second temps, l'impact d'une vague solitaire déferlante a été modélisé. Les pressions d'impact ont été déterminées et comparées avec celles issues d'expériences. Après une analyse numérique approfondie des simulations mono-phasiques, un modèle diphasique a été spécifiquement développé pour tenir compte à la fois des phases eau et air. Le modèle SPH diphasique a permis d'améliorer la qualité des résultats, notamment pour le cas « air pocket impact », où une poche d'air est emprisonnée lors de l'impact. Le but final de ce travail est d'étudier la survivabilité des récupérateurs d'énergie marine adossés à des structures côtières lors d'événements météorologiques violents. / The present manuscript focuses on the wave impact on a rigid wall in two dimensions. The numerical computations were performed using a Smoothed Particle Hydrodynamics (SPH) software named JOSEPHINE, developed at the LOMC laboratory. The software is based on a weakly-compressible SPH model, where Euler equation of motion is solved. Firstly, an academic test case, the impact of a triangular jet was used to validate and improve the numerical scheme to model violent impacts.The impact pressures were studied and compared to analytical and other numerical results. Secondly, the impact of a breaking solitary wave was modelled.The impact pressures were determined and compared with those obtained in the experiments. After a depth numerical analysis of mono-phase flow computations, a two-phase model was developed specifically to consider both water and air phases. The two-phase SPH model improved the results quality, especially for the case "air pocket impact", where an air pocket is trapped during the impact. The ultimate goal of this work is to study the survivability of coastal structures equipped with a marine energy recovery device during severe weather events.

L'approche Smoothed Particle Hydrodynamics (SPH) est une méthode de calcul pour simuler des écoulements fluides avec une méthode Lagrangienne de type suivi de particules. A l'inverse des méthodes Euleriennes, ce type d'approche ne nécessite pas de maillage. C'est là l'un des atouts majeurs de l'approche SPH puisqu'elle permet de s'affranchir des méthodes de suivi d'interfaces couramment utilisées dans les approches Euléeriennes (par exemple Volume-of-Fluid, Level-Set ou Front-Tracking). L'approche SPH est donc de plus en plus utilisée dans les domaines de l'hydro-ingénierie et de la géophysique notamment de part le traitement naturel des écoulements à surface libre dans la méthode SPH. Cependant, l'approche SPH n'est utilisée que depuis peu pour simuler des écoulements multiphasiques complexes et de nombreux problèmes restent en suspens, notamment concernant une formulation adéquate ou le micro-mélange aux interfaces. L'un des principaux enjeux de ces travaux de thèse est d'analyser de façon objective les différentes approches de type SPH existantes et d'évaluer leur capacité à simuler des écoulements multiphasiques complexes. Ainsi, la modélisation des phénomènes liés à la tension de surface a été réalisée et validée via l'utilisation de techniques de type Continuum Surface Force. Les phénomènes de convection naturelle ont quant à eux été modélisés grâce à une nouvelle formulation plus générale (non-Boussinesq). Une partie de ces travaux est dédiée à l'étude des problèmes de micro-mélange aux interfaces: les effets indésirables (notamment la fragmentation de l'interface) sont analysés et des solutions sont proposées. Une autre part de travail porte sur la modélisation des mouvements ascendants de bulles dans des liquides, avec l'inclusion des interactions entre bulles. Des simulations SPH ont été réalisées pour différents régimes d'écoulement, chacun d'eux correspondant à un ratio spécifique entre la tension de surface, la viscosité et la flottabilité. Les prédictions numériques de la topographie des bulles, de leur vitesse ainsi que de leur coefficient de trainée ont été validées. Pour ce faire, les résultats numériques ont été comparés non seulement aux données expérimentales de référence mais également à d'autres simulations numériques de bulles ascendantes. Dans ces travaux de thèse, une étude détaillée des concepts liés aux contraintes d'incompressibilité a été réalisée. Dans cet objectif, deux traitements différents ont été comparés: l'approche faiblement compressible (où une équation d'état adéquate est choisie) et l'approche incompressible (où une projection des champs de vitesse sur un espace sans divergence est réalisée de deux facons différentes). La pertinence de ces modèles pour des simulations d'écoulements multiphasiques est également évaluée. Les problèmes associés aux paramètres numériques sont discutés et un choix approprié de ces paramètres est proposé. Pour ce faire, de nombreux calculs de validation en deux et trois dimensions ont été réalisés. Enfin, une extension est proposée pour simuler les phénomènes liés à l'ébullition via une approche SPH. Ce sujet étant encore en friche, de nouvelles idées et schémas sont proposés pour le changement de phase liquide-vapeur dans l'approche SPH / Smoothed Particle Hydrodynamics (SPH) is a fully Lagrangian, particle based approach for fluid-flow simulations. One of its advantages over Eulerian techniques is no need of a numerical grid. Therefore, there is no necessity to handle the interface shape as it is done in Volume-of-Fluid, Lavel-Set or Front-Tracking methods. Thus, the SPH approach is increasingly used for hydro-engineering and geophysical applications involving free-surface flows where the natural treatment of evolving interfaces makes it an attractive method. However, for real-life multi-phase simulations this method has only started to be considered and many problems like a proper formulation or a spurious fragmentation of the interface remain to be solved. One of the aims of this work is to critically analyse the existing SPH variants and assess their suitability for complex multi-phase problems. For modelling the surface-tension phenomena the Continuum Surface Force (CSF) methods are validated and used. The natural convection phenomena are modeled using a new, more general formulation, beyond the Boussinesq approximation. A substantial part of the work is devoted to the problem of a spurious fragmentation of the interface (the micro-mixing of SPH particles). Its negative effects and possible remedies are extensively discussed and a new variant is proposed. Contrary to general opinion, it is proven that the micro-mixing is not only the problem of flows with neglegible surface tension. A significant part of this work is devoted to the modelling of bubbles rising through liquids, including bubble-bubble interactions. The SPH simulations were performed for several flow regimes corresponding to different relative importance of surface tension, viscosity and buoyancy effects. The predicted topological changes, bubble terminal velocity and drag coefficients were validated with respect to reference experimental data and compared to other numerical methods. In the work, fundamental concepts of assuring the incompressibility constraint in SPH are also recalled. An important part of work is a thorough comparison of two different incompressibility treatments: the weakly compressible approach, where a suitably chosen equation of state is used, and truly incompressible method (in two basic variants), where the velocity field is projected onto a divergence-free space. Their usefulness for multi-phase modelling is discussed. Problems associated with the numerical setup are investigated, and an optimal choice of the computational parameters is proposed and verified. For these purposes the study is supported by many two- and three-dimensional validation cases. In addition, the present work opens new perspectives to future simulations of boiling phenomena using the SPH method. First ideas and sketches for the implementation of the liquid-vapour phase change are presented

A two-dimensional axisymmetric implementation of the smoothed particle hydrodynamics (SPH) technique, called for short AxisSPH, has been described in this thesis, along with a number of basic tests and realistic applications. The main goal of this work was to fill a gap on a topic which has been scarcely addressed in the published literature concerning SPH. Although the application of AxisSPH to the simulation of real problems is restricted to those systems which display the appropriate symmetry there are, however, many interesting examples of physical systems which evolve following the axisymmetric premise. These examples belong to a variety of scientific and technological areas such as, for example, astrophysics, laboratory astrophysics or inertial confinement fusion. Additionally AxisSPH can be also useful in convergence studies of the standard 3D-SPH technique because the higher resolution achieved in 2D can be used to benchmark the three-dimensional codes. The main improvements implemented in AxisSPH with respect existing axisymmetric SPH formulations are summarized as follows: 1) We have derived simple analytical expressions for correction factors which largely improves the calculation of density and velocity in the vicinity of the z-axis. These expressions and their derivatives were given as a function of an adimensional parameter and do not increase the computational load of the scheme. 2) We have obtained the appropriate expression of the fluid Euler equations containing the new correction functions and their derivatives. Far enough from the singular axis, the scheme reduces to the standard formulation discussed by Brookshaw (2003). 3) A novel expression for the heat conduction term, which has to be added to the energy equation was devised and checked. This new term improves the description of the heat flux for those particles located at the axis neighborhoods. 4) Until now axisymmetric SPH hydrocodes handle artificial viscosity using a crude approach because it was treated as a simple restriction of the standard 3D Cartesian viscosity to 2D. Here we propose to calculate the viscous pressure as a combination of two terms, the first one is the (standard) Cartesian part and the second is the axis-converging part of the viscosity respectively. As expected this last term is of special relevance to simulate implosions. 5) We have developed an original method to incorporate gravity into AxisSPH. First the direct ring to ring force was found as a function of the Euclidean distance between the 2D particles. In second place the gravitational force on a given particle was obtained by summing the contributions of all N particles. We have also developed a more efficient scheme to obtain the gravitational force calculating the potential of the ring, instead the force because it involves lesser algebraic operations. The scheme has been checked using a large number of tests cases. These tests range from very specific oriented to check a particular algorithm or a piece of physics, to rather complex ones intended to analyze the behavior of the scheme in potential real applications (ICF, jets, astrophysics). At least in one case, the head on collision of a pair of white dwarfs, the result of the simulations carried out using AxisSPH brings new, unpublished, scientific material. / En esta tesis se ha desarrollado un código, que hemos llamado AxisSPH, en dos dimensiones axisimétrico a partir de la técnica conocida como SPH (“smooothed particle hydrodynamics”). AxisSPH ha sido validado después de realizar una serie de tests básicos y algunas simulaciones de situaciones reales. El objetivo principal de este trabajo ha sido llenar, en parte, el vacío existente al respecto en la literatura sobre SPH. Aunque sólo se puede aplicar AxisSPH en problemas reales que presenten la apropiada simetría, existen muchos ejemplos interesantes de sistemas físicos que presentan la simetría axial demandada. Existen ejemplos en campos de aplicación tanto científica como tecnológica, por ejemplo en astrofísica, en el llamado laboratorio de astrofísica o en fusión por confinamiento inercial (ICF). Otra interesante aplicación de AxisSPH puede ser su utilización en estudios de convergencia con otros códigos 3D-SPH debido a su mayor resolución, al tratarse de un código 2D. Las mejoras implementadas en el código AxisSPH en comparación con otros códigos axisimétricos SPH existentes se pueden resumir en los siguientes puntos: 1) Hemos deducido expresiones analíticas simples para unos factores de corrección que mejoran el cálculo de la densidad y la velocidad en las proximidades del eje z. Dichas expresiones y sus derivadas dependen de un parámetro adimensional que no incrementa mucho el peso computacional del esquema propuesto. 2) Hemos obtenido las expresiones adecuadas de las ecuaciones de Euler que contienen estas nuevas funciones correctoras y sus derivadas. Lejos del eje de singularidad estas ecuaciones se transforman en las de la formulación estándar propuesta por Brookshaw (2003). 3) Una expresión novedosa del término de conducción, que debe de añadirse a la ecuación de la energía, se ha propuesto y validado. Este nuevo término mejora la evolución del flujo de calor de las partículas situadas en las proximidades del eje z. 4) Hasta el momento los códigos hidrodinámicos SPH axisimétricos existentes trabajaban con una aproximación poco elaborada de la viscosidad artificial ya que consistían en una restricción a dos dimensiones de la viscosidad estándar 3D. En este trabajo proponemos el cálculo de la presión debida a la viscosidad como combinación de dos términos, el primero reflejo de la parte cartesiana y la segunda da cuenta de la parte relacionada con la convergencia en el eje. Como era de esperar este último término es de relevante importancia en la simulación de implosiones. 5) Hemos desarrollado un método original para incorporar el cálculo de la gravedad en el código AxisSPH. En primer lugar la fuerza directa de anillo a anillo y en segundo lugar la fuerza de la gravedad que sufre una determinada partícula a partir de la contribución del resto de las N partículas existentes. También hemos desarrollado un esquema más eficiente para calcular la gravedad a partir del cálculo del potencial del anillo en lugar del cálculo directo de la fuerza ya que implica un menor número de operaciones algebraicas. El método ha sido verificado con un gran número de test numéricos. Desde los más específicos orientados a comprobar la validez de un algoritmo particular o la capacidad para simular un fenómeno físico en particular, hasta simulaciones bastante más complejas, con la intención de validar la capacidad de simular aplicaciones potencialmente más reales (ICF, jets, astrofísica). Así, en al menos un caso, en la colisión frontal de dos enanas blancas, los resultados de la simulación utilizando AxisSPH pueden aportar material científico publicable.

Alumina is one of the most commonly used engineering ceramics for a variety of applications ranging from microelectronics to prosthetics due to its desirable properties. Unfortunately, conventional machining techniques generally lead to fracture, tool failure, low surface integrity, high energy consumption, low material removal rate, and high tool wear during machining due to high hardness and brittleness of the ceramic material. Laser machining offers an alternative for rapid processing of brittle and hard engineering ceramics. However, the material properties, especially the high thermal expansion coefficient and low thermal conductivity, may cause ceramic fracture due to thermal damage. Striation formation is another defect in laser cutting. These drawbacks limit advanced ceramics in engineering applications. In this work, various lasers and machining techniques are investigated to explore the feasibility of high-quality laser machining different thicknesses of alumina. The main contributions include: (i) Fibre laser crack-free cutting of thick-section alumina (up to 6-mm-thickness). A three-dimensional numerical model considering the material removal was developed to study the effects of process parameters on temperature, thermal-stress distribution, fracture initiation and propagation in laser cutting. A rapid parameters optimisation procedure for crack-free cutting of thick-section ceramics was proposed. (ii) Low power CW CO2 laser underwater machining of closed cavities (up to 2-mm depth) in alumina was demonstrated with high-quality in terms of surface finish and integrity. A three-dimensional thermal-stress model and a two-dimensional fluid smooth particle hydrodynamic model (SPH) were developed to investigate the physical processes during CO2 laser underwater machining. SPH modelling has been applied for the first time to studying laser processing of ceramics. (iii) Striation-free cutting of alumina sheets (1-mm thickness) is realised using a nano-second pulsed DPSS Nd: YAG laser, which demonstrates the capability of high average power short pulsed lasers in high-quality macro-machining. A mechanism of pulsed laser striation-free cutting was also proposed. The present work opens up new opportunities for applying lasers for high-quality machining of engineering ceramics.

Os métodos numéricos convencionais, baseados em malhas, têm sido amplamente aplicados na resolução de problemas da Dinâmica dos Fluidos Computacional. Entretanto, em problemas de escoamento de fluidos que envolvem superfícies livres, grandes explosões, grandes deformações, descontinuidades, ondas de choque etc., estes métodos podem apresentar algumas dificuldades práticas quando da resolução destes problemas. Como uma alternativa viável, existem os métodos de partículas livre de malhas. Neste trabalho é feita uma introdução ao método Lagrangeano de partículas, livre de malhas, Smoothed Particle Hydrodynamics (SPH) voltado para a simulação numérica de escoamentos de fluidos newtonianos compressíveis e quase-incompressíveis. Dois códigos numéricos foram desenvolvidos, uma versão serial e outra em paralelo, empregando a linguagem de programação C/C++ e a Compute Unified Device Architecture (CUDA), que possibilita o processamento em paralelo empregando os núcleos das Graphics Processing Units (GPUs) das placas de vídeo da NVIDIA Corporation. Os resultados numéricos foram validados e a eficiência computacional avaliada considerandose a resolução dos problemas unidimensionais Shock Tube e Blast Wave e bidimensional da Cavidade (Shear Driven Cavity Problem). / The conventional mesh-based numerical methods have been widely applied to solving problems in Computational Fluid Dynamics. However, in problems involving fluid flow free surfaces, large explosions, large deformations, discontinuities, shock waves etc. these methods suffer from some inherent difficulties which limit their applications to solving these problems. Meshfree particle methods have emerged as an alternative to the conventional grid-based methods. This work introduces the Smoothed Particle Hydrodynamics (SPH), a meshfree Lagrangian particle method to solve compressible flows. Two numerical codes have been developed, serial and parallel versions, using the Programming Language C/C++ and Compute Unified Device Architecture (CUDA). CUDA is NVIDIAs parallel computing architecture that enables dramatic increasing in computing performance by harnessing the power of the Graphics Processing Units (GPUs). The numerical results were validated and the speedup evaluated for the Shock Tube and Blast Wave one-dimensional problems and Shear Driven Cavity Problem.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho, foi desenvolvido um simulador numérico baseado no método livre de malhas Smoothed Particle Hydrodynamics (SPH) para a resolução de escoamentos de fluidos newtonianos incompressíveis. Diferentemente da maioria das versões existentes deste método, o código numérico faz uso de uma técnica iterativa na determinação do campo de pressões. Este procedimento emprega a forma diferencial de uma equação de estado para um fluido compressível e a equação da continuidade a fim de que a correção da pressão seja determinada. Uma versão paralelizada do simulador numérico foi implementada usando a linguagem de programação C/C++ e a Compute Unified Device Architecture (CUDA) da NVIDIA Corporation. Foram simulados três problemas, o problema unidimensional do escoamento de Couette e os problemas bidimensionais do escoamento no interior de uma Cavidade (Shear Driven Cavity Problem) e da Quebra de Barragem (Dambreak). / In this work a numerical simulator was developed based on the mesh-free Smoothed Particle Hydrodynamics (SPH) method to solve incompressible newtonian fluid flows. Unlike most existing versions of this method, the numerical code uses an iterative technique in the pressure field determination. This approach employs a differential state equation for a compressible fluid and the continuity equation to calculate the pressure correction. A parallel version of the numerical code was implemented using the Programming Language C/C++ and Compute Unified Device Architecture (CUDA) from the NVIDIA Corporation. The numerical results were validated and the speed-up evaluated for an one-dimensional Couette flow and two-dimensional Shear Driven Cavity and Dambreak problems.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho, foi desenvolvido um simulador numérico baseado no método livre de malhas Smoothed Particle Hydrodynamics (SPH) para a resolução de escoamentos de fluidos newtonianos incompressíveis. Diferentemente da maioria das versões existentes deste método, o código numérico faz uso de uma técnica iterativa na determinação do campo de pressões. Este procedimento emprega a forma diferencial de uma equação de estado para um fluido compressível e a equação da continuidade a fim de que a correção da pressão seja determinada. Uma versão paralelizada do simulador numérico foi implementada usando a linguagem de programação C/C++ e a Compute Unified Device Architecture (CUDA) da NVIDIA Corporation. Foram simulados três problemas, o problema unidimensional do escoamento de Couette e os problemas bidimensionais do escoamento no interior de uma Cavidade (Shear Driven Cavity Problem) e da Quebra de Barragem (Dambreak). / In this work a numerical simulator was developed based on the mesh-free Smoothed Particle Hydrodynamics (SPH) method to solve incompressible newtonian fluid flows. Unlike most existing versions of this method, the numerical code uses an iterative technique in the pressure field determination. This approach employs a differential state equation for a compressible fluid and the continuity equation to calculate the pressure correction. A parallel version of the numerical code was implemented using the Programming Language C/C++ and Compute Unified Device Architecture (CUDA) from the NVIDIA Corporation. The numerical results were validated and the speed-up evaluated for an one-dimensional Couette flow and two-dimensional Shear Driven Cavity and Dambreak problems.

Os métodos numéricos convencionais, baseados em malhas, têm sido amplamente aplicados na resolução de problemas da Dinâmica dos Fluidos Computacional. Entretanto, em problemas de escoamento de fluidos que envolvem superfícies livres, grandes explosões, grandes deformações, descontinuidades, ondas de choque etc., estes métodos podem apresentar algumas dificuldades práticas quando da resolução destes problemas. Como uma alternativa viável, existem os métodos de partículas livre de malhas. Neste trabalho é feita uma introdução ao método Lagrangeano de partículas, livre de malhas, Smoothed Particle Hydrodynamics (SPH) voltado para a simulação numérica de escoamentos de fluidos newtonianos compressíveis e quase-incompressíveis. Dois códigos numéricos foram desenvolvidos, uma versão serial e outra em paralelo, empregando a linguagem de programação C/C++ e a Compute Unified Device Architecture (CUDA), que possibilita o processamento em paralelo empregando os núcleos das Graphics Processing Units (GPUs) das placas de vídeo da NVIDIA Corporation. Os resultados numéricos foram validados e a eficiência computacional avaliada considerandose a resolução dos problemas unidimensionais Shock Tube e Blast Wave e bidimensional da Cavidade (Shear Driven Cavity Problem). / The conventional mesh-based numerical methods have been widely applied to solving problems in Computational Fluid Dynamics. However, in problems involving fluid flow free surfaces, large explosions, large deformations, discontinuities, shock waves etc. these methods suffer from some inherent difficulties which limit their applications to solving these problems. Meshfree particle methods have emerged as an alternative to the conventional grid-based methods. This work introduces the Smoothed Particle Hydrodynamics (SPH), a meshfree Lagrangian particle method to solve compressible flows. Two numerical codes have been developed, serial and parallel versions, using the Programming Language C/C++ and Compute Unified Device Architecture (CUDA). CUDA is NVIDIAs parallel computing architecture that enables dramatic increasing in computing performance by harnessing the power of the Graphics Processing Units (GPUs). The numerical results were validated and the speedup evaluated for the Shock Tube and Blast Wave one-dimensional problems and Shear Driven Cavity Problem.

This thesis presents a two-phase liquid-solid numerical model using Smoothed Particle Hydrodynamics (SPH). The scheme is developed for multi-phase flows in industrial tanks containing sediment used in the nuclear industry for decommissioning. These two-phase liquid-sediments flows feature a changing interfacial profile, large deformations and fragmentation of the interface with internal jets generating resuspension of the solid phase. SPH is a meshless Lagrangian discretization scheme whose major advantage is the absence of a mesh making the method ideal for interfacial and highly non-linear flows with fragmentation and resuspension. Emphasis has been given to the yield profile and rheological characteristics of the sediment solid phase using a yielding, shear and suspension layer which is needed to predict accurately the erosion phenomena. The numerical SPH scheme is based on the explicit treatment of both phases using Newtonian and non-Newtonian Bingham-type constitutive models. This is supplemented by a yield criterion to predict the onset of yielding of the sediment surface and a suspension model at low volumetric concentrations of sediment solid. The multi-phase model has been compared with experimental and 2-D reference numerical models for scour following a dry-bed dam break yielding satisfactory results and improvements over well-known SPH multi-phase models. A 3-D case using more than 4 million particles, that is to the author’s best knowledge one of the largest liquid-sediment SPH simulations, is presented for the first time. The numerical model is accelerated with the use of Graphic Processing Units (GPUs), with massively parallel capabilities. With the adoption of a multi-phase model the computational requirements increase due to extra arithmetic operations required to resolve both phases and the additional memory requirements for storing a second phase in the device memory. The open source weakly compressible SPH solver DualSPHysics was chosen as the platform for both CPU and GPU implementations. The implementation and optimisation of the multi-phase GPU code achieved a speed up of over 50 compared to a single thread serial code. Prior to this thesis, large resolution liquid-solid simulations were prohibitive and 3-D simulations with millions of particles were unfeasible unless variable particle resolution was employed. Finally, the thesis addresses the challenging problem of enforcing wall boundary conditions in SPH with a novel extension of an existing Modified Virtual Boundary Particle (MVBP) technique. In contrast to the MVBP method, the extended MVBP (eMVBP) boundary condition guarantees that arbitrarily complex domains can be readily discretized ensuring approximate zeroth and first order consistency for all particles whose smoothing kernel support overlaps the boundary. The 2-D eMVBP method has also been extended to 3-D using boundary surfaces discretized into sets of triangular planes to represent the solid wall. Boundary particles are then obtained by translating a full uniform stencil according to the fluid particle position and applying an efficient ray casting algorithm to select particles inside the fluid domain. No special treatment for corners and low computational cost make the method ideal for GPU parallelization. The models are validated for a number of 2-D and 3-D cases, where significantly improved behaviour is obtained in comparison with the conventional boundary techniques. Finally the capability of the numerical scheme to simulate a dam break simulation is also shown in 2-D and 3-D.